The average character degree and an improvement of the Ito-Michler theorem

2019/04/06 by Hung Ngoc Nguyen, Nguyen Ngoc Hung, Hung, Nguyen Ngoc +2
Engineering · Mathematics · #20D05 #20D10 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Primary 20C15 #Representation Theory (math.RT) #graph theory and CDMA systems #math.GR #math.RT #msc:20C15 #msc:20D05 #msc:20D10

paper · pdf · doi:10.48550/arxiv.1904.03574

19 pages

openalex publication_date 2019/04/06 · arxiv created 2019/04/07 · arxiv updated 2019/04/09 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

The classical Itô-Michler theorem states that the degree of every ordinary irreducible character of a finite group G is coprime to a prime p if and only if the Sylow p-subgroups of G are abelian and normal. In an earlier paper, we used the notion of average character degree to prove an improvement of this theorem for the prime p=2. In this follow-up paper, we obtain a full improvement for all primes.

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